zbMATH — the first resource for mathematics

Magnetohydrodynamic flow of a viscoelastic fluid. (English) Zbl 1220.76073
Summary: The non-linear differential equation for the magnetohydrodynamic Poiseuille flow of Phan-Thein-Tanner (PTT) conducting fluid is derived. Using the homotopy analysis method (HAM), the series solution is developed and its convergence is discussed. Also, the results are presented graphically and the effects of non-dimensional parameters on the flow field are analyzed. The results obtained reveal many interesting behaviors that warrant further study on the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

76W05 Magnetohydrodynamics and electrohydrodynamics
76A10 Viscoelastic fluids
34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
[1] Wang, Y.; Hayat, T.; Hutter, K., Int. J. non-linear mech., 40, 49, (2005) · Zbl 1349.76912
[2] Rajagopal, K.R., Mechanics of non-Newtonian fluids, () · Zbl 0818.76003
[3] Rajagopal, K.R.; Srinivasa, A.R., J. non-Newtonian fluid mech., 88, 207, (2000) · Zbl 0960.76005
[4] S.J. Liao, The proposed homotopy analysis technique for the solution of non-linear problems, PhD thesis, Shanghai Jiao Tong University, 1992
[5] Liao, S.J., Int. J. non-linear mech., 34, 759, (1999)
[6] Liao, S.J., Beyond perturbation: introduction to the homotopy analysis method, (2003), Chapman and Hall/CRC Press Boca Raton
[7] Liao, S.J., J. fluid mech., 488, 189, (2003)
[8] Liao, S.J., Appl. math. comput., 147, 499, (2004)
[9] Liao, S.J., Int. J. heat mass transfer, 48, 2529, (2005)
[10] Phan-Thein, N.; Tanner, R., J. non-Newtonian fluid mech., 2, 353, (1977)
[11] Phan-Thein, N., J. rheol., 22, 259, (1978)
[12] EL-Shehawey, E.F.; Elbarbary, Elsayed M.E.; Afifi, N.A.S.; Elshahed, M., Int. J. math. math. sci., 23, 795, (2000)
[13] A. Molabahrami, F. Khani, The homotopy analysis method to solve the Burgers-Huxley equation, Nonlinear Anal. Real World Appl., in press · Zbl 1167.35483
[14] Hayat, T.; Khan, M.; Asghar, S., Acta mechanica, 168, 213, (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.